Utility and Feasibility of Reasoning beyond Decidability in Semantic Technologies Sebastian Rudolph and Michael Schneider Institute AIFB, Karlsruhe Institute of Technology, DE rudolph@kit.edu FZI Research Center for Information Technology, Karlsruhe, DE schneid@fzi.de Abstract. Semantic Web knowledge representation standards such as RDF and OWL have gained momentum in the last years and are widely applied today. In the course of the standardization process of these and other knowledge representation formalisms, decidability of logical entail- ment has often been advocated as a central design criterion. On the other hand, restricting to decidable formalisms inevitably comes with constraints in terms of modeling power. Therefore, in this paper, we examine the requirement of decidability and weigh its importance in dif- ferent scenarios. Subsequently, we discuss a way to establish incomplete – yet useful – reasoning support for undecidable formalisms by deploying machinery from the successful domain of theorem proving in first-order predicate logic. While elaborating on the undecidable variants of the on- tology language OWL 2 as our primary examples, we argue that this approach could likewise serve as a role model for knowledge representa- tion formalisms from the Conceptual Structures community. 1 Introduction Today, the Semantic Web serves as the primary testbed for practical ap- plication of knowledge representation. A plethora of formalisms for repre- senting and reasoning with Web knowledge has been designed and stan- dardized under the auspices of the World Wide Web Consortium (W3C). While the early days of this endeavor saw ad-hoc and semantically under- specified approaches, interoperability requirements enforced their evolu- tion into mature logical languages with clearly specified formal semantics. In the process of defining more and more expressive such formalisms, an often-debated requirement is decidability of logical entailment, i.e. the principled existence of an algorithm that decides whether a body of knowl- edge has a certain proposition as a consequence. While it goes without saying that such an algorithm is clearly useful for all kind of querying or knowledge management tasks, results established back in the 1930s show